Question 13.10: Derivinga Sum-of-Products Expression from a Logic Circuit De...
Derivinga Sum-of-Products Expression from a Logic Circuit
Derive the truth table and minimum sum-of-products expression for the circuit of Figure 13.39.
Known Quantities: Logic circuit representing f(x, y, z).
Find: Expression for f and corresponding truth table.
Analysis: To determine the truth table, we write the expression corresponding to the logic circuit of Figure 13.39:
f=\bar{x} \cdot \bar{y}+y \cdot z
The truth table corresponding to this expression and the corresponding Karnaugh map with sum-of-products covering are shown in Figure 13.40.
Comments: If we used zeros in covering the Karnaugh map for this example, the resulting expression would be a product-of-sums. You may verify that, in the case of this example, the complexity of the circuit would be unchanged. Note also that there exists a third subcube (x=0, y z=01,11) that is not used because it does not help minimize the solution.
